The largest 4-digit and smallest 4-digit numbers formed by using the digits 4,0,3,7 (each digit used only once) respectively are_______.

Options

A. 4370, 4307
B. `3740,3047`
C. `7403,3704`
D. `7430,3047`

Answer

To solve the problem of finding the largest and smallest 4-digit numbers that can be formed using the digits 4, 0, 3, and 7 (with each digit used only once), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Digits**: The digits we have are 4, 0, 3, and 7.

2. **Finding the Largest 4-Digit Number**:
- To form the largest number, we should arrange the digits in descending order.
- The largest digit among the given numbers is 7, followed by 4, 3, and 0.
- Therefore, the largest 4-digit number is formed as follows:
- 7 (largest)
- 4 (next largest)
- 3
- 0
- Thus, the largest 4-digit number is **7430**.

3. **Finding the Smallest 4-Digit Number**:
- To form the smallest number, we need to arrange the digits in ascending order, but we must ensure that the first digit is not zero (as that would make it a 3-digit number).
- The smallest non-zero digit is 3. So we will start with 3.
- After placing 3, we can use the remaining digits in ascending order: 0, 4, and 7.
- Therefore, the smallest 4-digit number is formed as follows:
- 3 (smallest non-zero digit)
- 0
- 4
- 7
- Thus, the smallest 4-digit number is **3047**.

### Final Answer:
- The largest 4-digit number is **7430**.
- The smallest 4-digit number is **3047**.

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